Multiple choice

Minimum SOP of $\bar X \bar Y \bar Z + \bar X \bar Y Z + \bar XYZ + X \bar YZ+ XYZ$ is

  1. $XY+\bar XZ$
  2. $\bar X \bar Y+ YZ + XZ$
  3. $\bar X \bar Y + Z$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The minimum Sum of Products (SOP) form is X̄Ȳ + Z. Using Boolean algebra simplification or Karnaugh map: X̄ȲZ̄ + X̄ȲZ + X̄YZ + XȲZ + XYZ = X̄Ȳ(Z̄+Z) + X̄YZ + XȲZ + XYZ = X̄Ȳ + Z(X̄Y + XȲ + XY) = X̄Ȳ + Z(X̄Y + X(Ȳ+Y)) = X̄Ȳ + Z(X̄Y + X) = X̄Ȳ + Z(X + Y) = X̄Ȳ + XZ + YZ = X̄Ȳ + XZ + YZ. Further analysis shows X̄Ȳ + Z is the minimal form.

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